Questions regarding photons and distance contraction

I've got a few question regarding photons and lorentz contraction. they may be really stupid questions (I am not a physicist). But they have been bothering me for a while.

1. Is Lorentz distance contraction applicable to photons? If a photon travels to destination would it travel there instantly due to distance contraction? I realize that there is no frame of reference for a photon where it is at rest. So this question might be hypothetical.

2. If the answer to the above question is yes, then wouldn't that have caused photons that spawned right after the big bang to run out of space? Right after the big bang when Space Time was much smaller; won't this mean those photons could have ran out of space? Since those photons probably would not have encountered anything but vacuum, won't they reach the 'edge' instantly due to distance contraction

3. Now an extremely hypothetical question. Is it possible that photons(and other 0 mass particles) to have 0 velocity? And instead of them moving, Space-time moves towards or away from them? I am asking this because as they have 0 mass, they cannot be accelerated. Most papers I came across say that they travel at c the moment they are spawned until they are absorbed. So if we assume that they are actually not possessing any velocity and instead assume that everything else is moving toward or away from them will their interactions still follow the laws of physics?

I mean, for two particles with mass, you would get the same result if you assume either of them at rest and the other one moving. Is this applicable for photons as well?

1. The velocity of the light ray of photons is c for all observers.
2. At the same time, the spacetime interval of all lightlike phenomena such as photons is zero. That implies that the point of emission and the point of absorption are adjacent in spacetime!
3. If both points are adjacent, there is no place for a particle between them! As there is no particle, there can be no frame of reference.
4. The conclusion of this: A photon is a simple momentum which is transmitted directly between two particles which are adjacent in spacetime (linked by a lightlike interval). However, observers cannot observe spacetime intervals, they observe only the corresponding coordinates of space and time which permit to calculate the spacetime interval. That means that from their point of view, the place of emission and the place of absorption are not adjacent. Instead of the zero spacetime interval they observe an electromagnetic wave which is propagating at c and which is a sort of place holder between the place of emission and the place of absorption.

• So since space-time interval is always 0, does it matter how much distance the photon travels from our frame of reference. I mean weather its 1 light year or 1000 light years in our frame of reference, the Space-Time interval for the photon is still 0. That is where I have a problem. If all that is true, won't that hold true for infinite distance (in our frame of reference) as well. So it is technically possible for a photon to reach the edge of the universe - provided it does not get absorbed along the way? – Alwin Tom Mar 12 '19 at 7:33
• Also technically as far as a photon is considered it's velocity is 0, since space interval is 0. But at the same time infinity, since time interval is 0 as well? Boy that's weird. – Alwin Tom Mar 12 '19 at 7:34
• We know very little about the form and the precise evolution of the universe, so you are free to speculate on the answers, we gave you some hints. It seems that a photon needs always a target particle, a place of absorption. By the way, zero times infinity must not necessarily equal zero. – Moonraker Mar 12 '19 at 8:32
• Like I said these questions having been troubling me for a while. I tried talking with several smart people and doing some internet research, but nothing gave me any closure. But you are right, maybe we still no too little about everything around us. Thank you for taking your time and providing an answer. – Alwin Tom Mar 12 '19 at 8:45

1 Because photons have no rest frame, it doesn't make sense to talk about the distance or time they "experience", you can only talk about the distances and times that are measured between the photon emission and absorption in various rest frames. You can talk about the spacetime interval between the photon emission and absorption events, since the spacetime interval between two events is invariant (i.e., the same in all inertial reference frames), and for a photon that's always zero. However, it's not very useful to say that two events that are separated by a null spacetime interval are adjacent.

2 Space doesn't have an edge, and it didn't have one immediately after the Big Bang, either. Also, in that early era the energy density of the universe was very high, so the matter in the universe was incandescent, so photons couldn't travel very far. It took about 380,000 years for matter to cool down sufficiently (via the expansion of space) before the universe became transparent, during the era of recombination, when the radiation that we now detect as the Cosmic Microwave Background was first released.

3 The Lorentz transformation lets us transform between inertial reference frames, that is, we can use it to transform velocities from one rest frame to another rest frame. But since photons don't have a rest frame you cannot use it to say that photons are at rest and other bodies are in motion.

BTW, if something has no mass, in Newtonian physics any force gives it infinite acceleration. $$F=ma$$, so $$a=F/m$$. Formally, division by zero is undefined, but we can say that as $$m$$ approaches 0, $$a$$ approaches infinity.

1. Yes. Objects that travel at the speed of light experience infinite length contraction and infinite time dilation.

2. No. The universe doesn’t have an edge. It either extends to infinity or curves back on itself in the current cosmological model.

3. No. A massless particle with zero velocity, or a nonzero velocity less than the speed of light or greater than the speed of light, would have no energy and no momentum, so it would be the same as nothingness. Massless particles only have energy and momentum when they travel at the speed of light.

• Thank you for answering. But I am not entirely clear about the answer for (2). If lorentz distance contraction is applicable for photons then all distances, even infinity, would contract to 0 won't it? Also as far as I understood, the universe expanded after the big bang. So right after the big bang shouldn't it have a finite size? – Alwin Tom Mar 12 '19 at 6:50
• An infinite distance contracted infinitely is indeterminate. You can’t say what $\infty/\infty$ is. The size of the observable part of the universe is finite. The size of the entire universe is finite if it has positive curvature and infinite if it has zero or negative curvature. In the latter case, it is infinite at every instant except $t=0$. Observational evidence is that the curvature seems to be zero or very close to it. Even if the size of the entire universe is finite, it has no edge for photons to reach. – G. Smith Mar 12 '19 at 15:49